The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  0  2  1  0  1  1  2 12  8  1  1  1  1  4  1  8  1  1  2
 0  2  0  6  4  6 12  2  8 14  4  6  0  2  2 14  2  6 12  2 12  6  6  2  2 14  8  4  4  8 14  4  0  6  6
 0  0 12  0  4  0  0  0  8  4  8 12  4  4  4  0 12  4  0  8  8 12  8  0  8  4  4  0  4 12  8  4 12  0  8
 0  0  0 12  0  0  0  4 12  8  4 12 12  8  0  4 12 12 12  0  0  4  8  8  4  8 12  0 12 12 12  8  4 12  8
 0  0  0  0  8  0  0  0  0  8  0  8  8  0  0  8  0  0  8  0  8  0  8  0  8  0  8  8  0  8  8  0  0  0  8
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  8  8  0  8  8  8  0  8  0  0  8  8
 0  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  0  8  0  8  8  0  8  0  8  0  0  8  8

generates a code of length 35 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+138x^28+52x^29+472x^30+476x^31+1416x^32+1540x^33+2564x^34+2988x^35+2666x^36+1660x^37+1388x^38+372x^39+404x^40+76x^41+108x^42+4x^43+44x^44+12x^46+3x^48

The gray image is a code over GF(2) with n=280, k=14 and d=112.
This code was found by Heurico 1.16 in 2.61 seconds.